# Chains of Interacting Solitons

## Abstract

**:**

## 1. Introduction

## 2. Chains of Kinks

## 3. Chains of Baby Skyrmions

## 4. Chains of Skyrmions

## 5. Chains of Q-Balls and Boson Stars

## 6. Monopole–Anti-Monopole Chains

## 7. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**${\varphi}^{4}$ kink–antikink pair bounded by fermions. Profiles of the scalar field and fermion density distribution of the collective mode at $g=1$ (left plot) and scalar field of the configuration bounded to this mode vs. Yukawa coupling g (right plot). Reprinted (without modification) from [38], with permission of APS.

**Figure 2.**${\varphi}^{6}$ multi-kink configurations bounded by fermions. Profiles of the scalar field and fermion density distribution of the collective fermionic mode(left plot) and the chain of the kinks $(-1,1)+(1,-1)+(-1,1)$ bounded to the higher fermionic mode (right plot). Reprinted (without modification) from the work in [38], with permission of APS.

**Figure 3.**Contour plots of the energy density distributions of the solutions of the planar Skyrme model with the potential (12) in the sectors of degrees $Q=3\u20136$ and $Q=10$.

**Figure 6.**Skyrmion–anti-Skyrmion chains. Reprinted (without modification) from the work in [26], with STM Permission.

**Figure 7.**Chains of boson stars: Energy density isosurfaces on the fundamental branch for $\alpha =0.25$ at $\omega =0.80$ (in different scales).

**Figure 8.**Axially-symmetric $n=1$ chain of gauged Q-balls: The field components X (upper left) and Y (upper right), the electric charge density distribution (bottom left), and the magnitude of the magnetic field distribution (bottom right) of the $k=6$ chain [85].

**Figure 9.**Monopole–anti-monopole chains: The magnetic charge density distributions (upper plots), the energy density distributions (middle plots)) and the magnitude of the Higgs field (bottom plots), of the $n=1,m=3$ and $n=1,m=6$ chains.

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Shnir, Y.M.
Chains of Interacting Solitons. *Symmetry* **2021**, *13*, 284.
https://doi.org/10.3390/sym13020284

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Shnir YM.
Chains of Interacting Solitons. *Symmetry*. 2021; 13(2):284.
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**Chicago/Turabian Style**

Shnir, Yakov M.
2021. "Chains of Interacting Solitons" *Symmetry* 13, no. 2: 284.
https://doi.org/10.3390/sym13020284